Markov Chain Monte Carlo Based Analysis of Bearing Vibrations

MCMC;bearings;vibration;time-domain;frequency-domain

Lawrence, Hilary Jane ; Molteno, Tim ; Fox, Colin

University of Otago

关键词: MCMC;    bearings;    vibration;    time-domain;    frequency-domain;   

Others  :  https://ourarchive.otago.ac.nz/bitstream/10523/6214/1/LawrenceHilaryJ2016PhD.pdf

美国|英语

来源: Otago University Research Archive

【 摘 要 】

The aim of the work in this thesis is to use bearing vibration data to infer the condition of bearings, in particular to detect the presence or absence of damage, and identify the location and cause of damage to parts of the bearing structure. Traditional methods of vibration analysis are evaluated and compared with Markov chain Monte Carlo (MCMC) methods.The vibration datasets come from a selection of bearings that have been run from new. After running-in bearings, some are allowed to continue running for several hours. Others have seeded defects applied to balls or bearing races, and are then run for a short time. These data are used to evaluate the effectiveness of time-domain, frequency-domain and MCMC methods in the field of bearing vibration analysis.Time-domain measures can detect the presence or absence of damage in most cases. Different defect types affect vibrations differently, and this can be seen in plots of vibration data. Theconventional time-domain methods investigated take a discrete measure or measures over each data. They are simple to implement, but do not have the ability to detect these differences in vibrations, and therefore cannot detect the nature of damage.Analysis in the frequency-domain is based on the fast Fourier transform (FFT) and filtering. It is successful in detecting the nature of some defects. Bearings with some defect types, or with low levels of damage, are difficult to distinguish from undamaged bearings, and each defect type is better detected using different filtering. These differences suggest that prominent vibrations occur at modes of flexural vibration of the outer race, and that the inner race can be approximated as a rigid body. A classification scheme is implemented using a mixture of time-domain and frequency-domain measures. This scheme can correctly classify data from many - but not all - bearings, but it gives no information on the certainty of classifications.The findings from the time-domain and frequency-domain analysis have been well explored previously. In this thesis they are combined with Bayesian inference, using a correlation based measure of likelihood to infer bearing condition. MCMC methods are implemented using an adaptive Metropolis (AM) algorithm, existing models of bearing behaviour, and vibration data in the time-domain. MCMC outputs give estimations of the empirical marginal distribution of parameters, so that not only can parameter values - and therefore the underlying physical mechanism - be estimated, but uncertainties on these estimates can also be quantified.An aims of this thesis is to see whether MCMC methods can be used to infer properties of bearing condition. This thesis shows this is possible, but there are difficulties to overcome. In particular, the use of the correlation based measure of likelihood results in the chain failing to converge in some cases. These states are identifiable, as the likelihood is lower than when convergence occurs. Possible solutions to this problem are discussed.Analysis of MCMC outputs leads to model refinements to better measure bearing properties. Marginal distributions relating to vibration frequency have properties that allow the physical cause of vibration sources to be inferred. Using data in the time-domain has some advantages when separating the individual sources of these periodic vibrations. In the frequency domain some of these sources have harmonics or sidebands that coincide with predicted frequencies of other sources. In addition, some of these frequencies are not at their predicted values. This is not unexpected, as slippage and the effect of loads are known to alter these frequencies. The analysis of MCMC outputs allows the physical cause of discrepancies to be investigated. Vibrations during the normal operation of undamaged bearings have certain properties that differ from vibrations caused by bearing defects, and relevant parameters show these differences. Distributions of parameters relating to the amplitude and duration of vibrations caused by defects are shown to have a relationship to defect dimensions. Further development is required before defect dimensions can be directly inferred.This thesis shows that traditional methods of vibration analysis can distinguish between damaged and undamaged bearings in most cases, and detect the nature of damage in some cases. MCMC methods have potential in the field of bearing vibration analysis, and can provide meaningful inference of the physical properties of bearings.